O
abs
acos
acosh
addell(e,z1,z2)=elladd(e,z1,z2);
addprimes
adj(x)=matadjoint(x);
agm
akell(e,n)=ellak(e,n);
algdep
algdep2(x,n,dec)=algdep(x,n,dec);
algtobasis(nf,x)=nfalgtobasis(nf,x);
allocatemem
anell(e,n)=ellan(e,n);
apell(e,n)=ellap(e,n);
apell2(e,n)=ellap(e,n,1);
apprpadic(x,a)=padicappr(x,a);
arg
asin
asinh
assmat(x)=matcompanion(x);
atan
atanh
basis(x)=nfbasis(x);
basis2(x)=nfbasis(x,2);
basistoalg(nf,x)=nfbasistoalg(nf,x);
bernreal
bernvec
bestappr
bezout
bezoutres
bigomega
bilhell(e,z1,z2)=ellbil(e,z1,z2);
bin(x,y)=binomial(x,y);
binary
bittest
boundcf(x,lmax)=contfrac(x,,lmax);
boundfact(x,lim)=factor(x,lim);
box(x,a)=plotbox(x,a);
buchcertify(bnf)=bnfcertify(bnf);
buchfu(bnf)=bnfunit(bnf);
buchgen(P)=bnfclassunit(P,2);
buchgenforcefu(P)=bnfclassunit(P,1);
buchgenfu(P)=bnfclassunit(P);
buchimag(D,c1,c2,g)=quadclassunit(D,,[c1,c2,g]);
buchinit(P)=bnfinit(P,2);
buchinitforcefu(P)=bnfinit(P,1);
buchinitfu(P)=bnfinit(P);
buchnarrow(bnf)=bnfnarrow(bnf);
buchray(bnf,ideal)=bnrclass(bnf,ideal);
buchrayinit(bnf,ideal)=bnrclass(bnf,ideal,1);
buchrayinitgen(bnf,ideal)=bnrclass(bnf,ideal,2);
buchreal(D)=quadclassunit(D);
bytesize(x)=sizebyte(x);
ceil
centerlift
cf(x)=contfrac(x);
cf2(b,x)=contfrac(x,b);
changevar
char(x,y)=charpoly(x,y);
char1(x,y)=charpoly(x,y,1);
char2(x,y)=charpoly(x,y,2);
chell(x,y)=ellchangecurve(x,y);
chinese
chptell(x,y)=ellchangepoint(x,y);
classno(x)=qfbclassno(x);
classno2(x)=qfbclassno(x,1);
coeff(x,s)=polcoeff(x,s);
color(w,c)=plotcolor(w,c);
compimag(x,y)=x*y;
compo(x,s)=component(x,s);
compositum(pol1,pol2)=polcompositum(pol1,pol2);
compositum2(pol1,pol2)=polcompositum(pol1,pol2,1);
comprealraw(x,y)=qfbcompraw(x,y);
concat
conductor(a1)=bnrconductor(a1);
conductorofchar(bnr,chi)=bnrconductorofchar(bnr,chi);
conj
conjvec
content
convol(x,y)=serconvol(x,y);
core
core2(x)=core(x,1);
coredisc
coredisc2(x)=coredisc(x,1);
cos
cosh
cursor(w)=plotcursor(w);
cvtoi(x)=truncate(x,&e);
cyclo(n)=polcyclo(n);
decodefactor(fa)=factorback(fa);
decodemodule(nf,fa)=bnfdecodemodule(nf,fa);
default
degree(x)=poldegree(x);
denom(x)=denominator(x);
deplin(x)=lindep(x,-1);
deriv
det(x)=matdet(x);
det2(x)=matdet(x,1);
detint(x)=matdetint(x);
diagonal(x)=matdiagonal(x);
dilog
dirdiv
direuler
dirmul
dirzetak
disc(x)=poldisc(x);
discf(x)=nfdisc(x);
discf2(x)=nfdisc(x,2);
discrayabs(bnr,subgroup)=bnrdisc(bnr,subgroup);
discrayabscond(bnr)=bnrdisc(bnr,,,2);
discrayabslist(bnf,list)=bnrdisclist(bnf,list);
discrayabslistarch(bnf,arch,bound)=bnrdisclist(bnf,bound,arch);
discrayabslistarchall(bnf,bound)=bnrdisclist(bnf,bound,,1);
discrayabslistlong(bnf,bound)=bnrdisclist(bnf,bound);
discrayrel(bnr,subgroup)=bnrdisc(bnr,subgroup,,1);
discrayrelcond(bnr,subgroup)=bnrdisc(bnr,subgroup,,3);
divisors
divres(x,y)=divrem(x,y);
divsum(n,X,expr)=sumdiv(n,X,expr);
draw(list)=plotdraw(list);
eigen(x)=mateigen(x);
eint1
erfc
eta
euler=Euler;
eval
exp
extract(x,y)=vecextract(x,y);
fact(x)=factorial(x);
factcantor(x,p)=factorcantor(x,p);
factfq(x,p,a)=factorff(x,p,a);
factmod(x,p)=factormod(x,p);
factor
factoredbasis(x,p)=nfbasis(x,,p);
factoreddiscf(x,p)=nfdisc(x,,p);
factoredpolred(x,p)=polred(x,,p);
factoredpolred2(x,p)=polred(x,2,p);
factornf
factorpadic
factorpadic2(x,p,r)=factorpadic(x,p,r,1);
factpol(x,l,hint)=factor(x);
factpol2(x,l,hint)=factor(x);
fibo(x)=fibonacci(x);
floor
for
fordiv
forprime
forstep
forvec
fpn(p,n)=ffinit(p,n);
frac
galois(x)=polgalois(x);
galoisapply(nf,aut,x)=nfgaloisapply(nf,aut,x);
galoisconj(nf)=nfgaloisconj(nf);
galoisconj1(nf)=nfgaloisconj(nf,2);
galoisconjforce=nfgaloisconj(nf,1);
gamh(x)=gammah(x);
gamma
gauss(a,b)=matsolve(a,b);
gaussmodulo(M,D,Y)=matsolvemod(M,D,Y);
gaussmodulo2(M,D,Y)=matsolvemod(M,D,Y,1);
gcd
getheap
getrand
getstack
gettime
globalred(x,y)=ellglobalred(x,y);
goto=;
hclassno(x)=qfbhclassno(x);
hell(e,x)=ellheight(e,x);
hell2(e,x)=ellheight(e,x,1);
hermite(x)=mathnf(x);
hermite2(x)=mathnf(x,1);
hermitehavas(x)=mathnf(x,2);
hermitemod(x,d)=mathnfmod(x,d);
hermitemodid(x,d)=mathnfmodid(x,d);
hermiteperm(x)=mathnf(x,3);
hess(x)=mathess(x);
hilb(x,y)=hilbert(x,y);
hilbert(n)=mathilbert(n);
hilbp(x,y,p)=hilbert(x,y,p);
hvector(n,X,expr)=vector(n,X,expr);
hyperu
i=I;
idealadd
idealaddmultone(nf,list)=idealaddtoone(nf,list);
idealaddone(nf,x,y)=idealaddtoone(nf,x,y);
idealappr
idealapprfact(nf,x)=idealappr(nf,x,1);
idealchinese
idealcoprime
idealdiv
idealdivexact(nf,x,y)=idealdiv(nf,x,y,1);
idealfactor
idealhermite(nf,x)=idealhnf(nf,x);
idealhermite2(nf,x)=idealhnf(nf,x);
idealintersect
idealinv
idealinv2(nf,x)=idealinv(nf,x,1);
ideallist
ideallistarch
ideallistarchgen(nf,list,arch)=ideallistarch(nf,list,arch,1);
ideallistunit(nf,list)=ideallist(nf,list,2);
ideallistunitarch=ideallistarch(nf,list,arch,2);
ideallistunitarchgen=ideallistarch(nf,list,arch,3);
ideallistunitgen=ideallist(nf,list,3);
ideallistzstar(nf,bound)=ideallist(nf,bound);
ideallistzstargen(nf,bound)=ideallist(nf,bound,1);
ideallllred(nf,x,vdir)=idealred(nf,x,vdir);
idealmul
idealmulred(nf,x,y)=idealmul(nf,x,y,1);
idealnorm
idealpow
idealpowred(nf,x,y)=idealpow(nf,x,y,1);
idealtwoelt
idealtwoelt2(nf,x,a)=idealtwoelt(nf,x,a);
idealval
idmat(n)=matid(n);
if
imag
image(x)=matimage(x);
image2(x)=matimage(x,1);
imagecompl(x)=matimagecompl(x);
incgam
incgam1(s,x)=;
incgam2(s,x)=;
incgam3(s,x)=;
incgam4(s,x,y)=incgam(s,x,y);
indexrank(x)=matindexrank(x);
indsort(x)=vecsort(x,,1);
initalg(pol)=nfinit(pol);
initalgred(x)=nfinit(x,2);
initalgred2(x)=nfinit(x,3);
initell(x)=ellinit(x);
initrect(w,x,y)=plotinit(w,x,y);
initzeta(x)=zetakinit(x);
integ(x,y)=intformal(x,y);
intersect(x,y)=matintersect(x,y);
intgen(x=a,b,s)=intnum(x=a,b,s,1);
intinf(x=a,b,s)=intnum(x=a,b,s,2);
intnum
intopen(x=a,b,s)=intnum(x=a,b,s,3);
inverseimage(x,y)=matinverseimage(x,y);
isdiagonal(x)=matisdiagonal(x);
isfund(x)=isfundamental(x);
isideal(nf,x)=nfisideal(nf,x);
isincl(x,y)=nfisincl(x,y);
isinclfast(nf1,nf2)=nfisincl(nf1,nf2,1);
isirreducible(x)=polisirreducible(x);
isisom(x,y)=nfisisom(x,y);
isisomfast(x,y)=nfisisom(x,y);
isoncurve(e,x)=ellisoncurve(e,x);
isprime
isprincipal(bnf,x)=bnfisprincipal(bnf,x,0);
isprincipalforce(bnf,x)=bnfisprincipal(bnf,x,2);
isprincipalgen(bnf,x)=bnfisprincipal(bnf,x);
isprincipalgenforce(bnf,x)=bnfisprincipal(bnf,x,3);
isprincipalray(bnf,x)=bnrisprincipal(bnf,x);
isprincipalraygen
ispsp(x)=ispseudoprime(x);
isqrt(x)=sqrtint(x);
isset(x)=setisset(x);
issqfree(x)=issquarefree(x);
issquare
isunit(bnf,x)=bnfisunit(bnf,x);
jacobi(x)=qfjacobi(x);
jbesselh(n,x)=besseljh(n,x);
jell(x)=ellj(x);
karamul(x,y,k)=;
kbessel(nu,x)=besselk(nu,x);
kbessel2(nu,x)=besselk(nu,x,1);
ker(x)=matker(x);
keri(x)=matker(x,1);
kerint(x)=matkerint(x);
kerint1(x)=matkerint(x,1);
kerint2(x)=matkerint(x,2);
kill
killrect(w)=plotkill(w);
kro(x,y)=kronecker(x,y);
label=;
lambdak(nfz,s)=zetak(nfz,s,1);
laplace(x)=serlaplace(x);
lcm
legendre(n)=pollegendre(n);
length
lex
lexsort(x)=vecsort(x,,2);
lift
lindep
lindep2(x)=lindep(x,1);
line(w,x2,y2)=plotlines(w,x2,y2);
lines(w,x2,y2)=plotlines(w,x2,y2);
lll(x)=qflll(x);
lll1(x)=qflll(x,7);
lllgen(x)=qflll(x,8);
lllgram(x)=qflllgram(x);
lllgram1(x)=qflllgram(x,7);
lllgramgen(x)=qflllgram(x,8);
lllgramint(x)=qflllgram(x,1);
lllgramkerim(x)=qflllgram(x,4);
lllgramkerimgen(x)=qflllgram(x,5);
lllint(x)=qflll(x,1);
lllintpartial(x)=qflll(x,2);
lllkerim(x)=qflll(x,4);
lllkerimgen(x)=qflll(x,5);
lllrat(x)=qflll(x,3);
ln(x)=log(x);
lngamma
localred(e)=elllocalred(e);
log
logagm(x)=log(x,1);
lseriesell(e,s,N,A)=elllseries(e,s,A);
makebigbnf(sbnf)=bnfmake(sbnf);
mat(x)=Mat(x);
matextract(x,y,z)=vecextract(x,y,z);
mathell(e,x)=ellheightmatrix(e,x);
matrix
matrixqz
matrixqz2(x,p)=matrixqz(x,-1);
matrixqz3(x,p)=matrixqz(x,-2);
matsize
max
min
minideal(nf,ix,vdir)=idealmin(nf,ix,vdir);
minim(x,bound,maxnum)=qfminim(x,bound,maxnum);
minim2(x,bound)=qfminim(x,bound,,1);
mod(x,y)=Mod(x,y);
modp(x,y,p)=Mod(x,y,1);
modreverse
modulargcd(x,y)=gcd(x,y,1);
move(w,x,y)=plotmove(w,x,y);
mu(n)=moebius(n);
newtonpoly
nextprime
nfdetint
nfdiv(nf,a,b)=nfeltdiv(nf,a,b);
nfdiveuc(nf,a,b)=nfeltdiveuc(nf,a,b);
nfdivres(nf,a,b)=nfeltdivrem(nf,a,b);
nfhermite(nf,x)=nfhnf(nf,x);
nfhermitemod(nf,x,detx)=nfhnfmod(nf,x,detx);
nfmod(nf,a,b)=nfeltmod(nf,a,b);
nfmul(nf,a,b)=nfeltmul(nf,a,b);
nfpow(nf,a,k)=nfeltpow(nf,a,k);
nfreduce(nf,a,id)=nfeltreduce(nf,a,id);
nfsmith(nf,x)=nfsnf(nf,x);
nfval(nf,a,pr)=nfeltval(nf,a,pr);
norm
norml2
nucomp(x,y,l)=qfbnucomp(x,y,l);
numdiv
numer(x)=numerator(x);
nupow(x,n)=qfbnupow(x,n);
o(x)=O(x);
omega
ordell(e,x)=ellordinate(e,x);
order(x)=znorder(x);
orderell(e,x)=ellorder(e,x);
ordred(x)=polredord(x);
padicprec
pascal(n)=matpascal(n);
perf(a)=qfperfection(a);
permutation(n,k)=numtoperm(n,k);
permutation2num(vect)=permtonum(vect);
pf(x,p)=qfbprimeform(x,p);
phi(x)=eulerphi(x);
pi=Pi;
plot
ploth
ploth2(X=a,b,expr)=ploth(X=a,b,expr,1);
plothmult(X=a,b,expr)=ploth(X=a,b,expr);
plothraw
pnqn(x)=contfracpnqn(x);
point(w,x,y)=plotpoints(w,x,y);
pointell(e,z)=ellztopoint(e,z);
points(w,x,y)=plotpoints(w,x,y);
polint(xa,ya,x)=polinterpolate(xa,ya,p);
polred
polred2(x)=polred(x,2);
polredabs
polredabs2(x)=polredabs(x,1);
polredabsall(x)=polredabs(x,4);
polredabsfast(x)=polredabs(x,8);
polredabsnored(x)=polredabs(x,2);
polsym
polvar(x)=variable(x);
poly(x,v)=Pol(x,v);
polylog
polylogd(m,x)=polylog(m,x,1);
polylogdold(m,x)=polylog(m,x,2);
polylogp(m,x)=polylog(m,x,3);
polyrev(x,v)=Polrev(x,v);
polzag(n,m)=polzagier(n,m);
postdraw(list)=psdraw(list);
postploth(X=a,b,expr)=psploth(X=a,b,expr);
postploth2(X=a,b,expr)=psploth(X=a,b,expr,1);
postplothraw(listx,listy)=psplothraw(listx,listy);
powell(e,x,n)=ellpow(e,x,n);
powrealraw(x,n)=qfbpowraw(x,n);
pprint(x)=printp(x);
pprint1(x)=printp1(x);
prec(x,n)=precision(x,n);
precision
prime
primedec(nf,p)=idealprimedec(nf,p);
primes
primroot(n)=znprimroot(n);
principalideal(nf,x)=idealprincipal(nf,x);
principalidele(nf,x)=ideleprincipal(nf,x);
print
print1
prod(x,X=a,b,expr)=prod(X=a,b,expr,x);
prodeuler
prodinf
prodinf1(X=a,expr)=prodinf(X=a,expr,1);
psi
qfi(a,b,c)=Qfb(a,b,c);
qfr(a,b,c,d)=Qfb(a,b,c,d);
quaddisc
quadgen
quadpoly
random
rank(x)=matrank(x);
rayclassno(bnf,x)=bnrclassno(bnf,x);
rayclassnolist(bnf,liste)=bnrclassnolist(bnf,liste);
rbox(w,dx,dy)=plotrbox(w,dx,dy);
read(x)=input(x);
real
recip(x)=polrecip(x);
redimag(x)=qfbred(x);
redreal(x)=qfbred(x);
redrealnod(x,d)=qfbred(x,2,,d);
reduceddisc(f)=poldiscreduced(f);
regula(x)=quadregulator(x);
reorder
resultant(x,y)=polresultant(x,y);
resultant2(x,y)=polresultant(x,y,1);
reverse(x)=serreverse(x);
rhoreal(x)=qfbred(x,1);
rhorealnod(x,d)=qfbred(x,3,,d);
rline(w,dx,dy)=plotrline(w,dx,dy);
rlines(w,dx,dy)=plotrlines(w,dx,dy,1);
rmove(w,dx,dy)=plotrmove(w,dx,dy);
rndtoi(x)=round(x,&e);
rnfbasis
rnfdiscf(nf,pol)=rnfdisc(nf,pol);
rnfequation
rnfequation2(nf,pol)=rnfequation(nf,pol,1);
rnfhermitebasis(bnf,order)=rnfhnfbasis(bnf,order);
rnfisfree
rnflllgram
rnfpolred
rnfpseudobasis
rnfsteinitz
rootmod(x,p)=polrootsmod(x,p);
rootmod2(x,p)=polrootsmod(x,p,1);
rootpadic(x,p,r)=polrootspadic(x,p,r);
roots(x)=polroots(x);
rootsof1(nf)=nfrootsof1(nf);
rootsold(x)=polroots(x,1);
round
rounderror(x)=round(x,&e);
rpoint(w,dx,dy)=plotrpoint(w,dx,dy);
rpoints(w,dx,dy)=plotrpoints(w,dx,dy);
scale(w,x1,x2,y1,y2)=plotscale(w,x1,x2,y1,y2);
series(x,v)=Ser(x,v);
set(x)=Set(x);
setintersect
setminus
setprecision(n)=default(realprecision,n);
setrand
setsearch
setserieslength(n)=default(seriesprecision,n);
settype(x,t)=type(x,t);
setunion
shift
shiftmul
sigma
sigmak(x,k)=sigma(x,k);
sign
signat(x)=qfsign(x);
signunit(bnf)=bnfsignunit(bnf);
simplefactmod(x,p)=factormod(x,p,1);
simplify
sin
sinh
size(x)=sizedigit(x);
smallbasis(x)=nfbasis(x,1);
smallbuchinit(x)=bnfinit(x,3);
smalldiscf(x)=nfdisc(x,1);
smallfact(x)=factor(x,0);
smallinitell(x)=ellinit(x,1);
smallpolred(x)=polred(x,1);
smallpolred2(x)=polred(x,3);
smith(x)=matsnf(x);
smith2(x)=matsnf(x,1);
smithclean(x)=matsnf(x,4);
smithpol(x)=matsnf(x,2);
solve
sort(x)=vecsort(x);
sqr
sqred(x)=qfgaussred(x);
sqrt
srgcd(x,y)=gcd(x,y,2);
string(w,x)=plotstring(w,x);
sturm(x)=polsturm(x);
sturmpart(x,a,b)=polsturm(x,a,b);
subcyclo(p,d)=polsubcyclo(p,d);
subell(e,a,b)=ellsub(e,a,b);
subst
sum(x,X=a,b,expr)=sum(X=a,b,expr,x);
sumalt
sumalt2(X=a,expr)=sumalt(X=a,expr,1);
suminf
sumpos
sumpos2(X=a,expr)=sumpos(X=a,expr,1);
supplement(x)=matsupplement(x);
sylvestermatrix(x,y)=polsylvestermatrix(x,y);
system
tan
tanh
taniyama(e)=elltaniyama(e);
taylor
tchebi(n)=poltchebi(n);
teich(x)=teichmuller(x);
texprint(x)=printtex(x);
theta
thetanullk
threetotwo=;
threetotwo2=;
torsell(e)=elltors(e);
trace
trans(x)=mattranspose(x);
trunc(x)=truncate(x);
tschirnhaus(x)=poltschirnhaus(x);
twototwo(nf,a,b)=;
type
unit(x)=quadunit(x);
until
valuation
vec(x)=Vec(x);
vecindexsort(x)=vecsort(x,,1);
veclexsort(x)=vecsort(x,,2);
vecmax
vecmin
vecsort
vector
vvector(n,X,expr)=vectorv(n,X,expr);
weipell(e)=ellwp(e);
wf(x)=weber(x);
wf2(x)=weber(x,2);
while
zell(e,P)=ellpointtoz(e,P);
zeta
zetak
zideallog(nf,x,bid)=ideallog(nf,x,bid);
zidealstar(nf,I)=idealstar(nf,I);
zidealstarinit(nf,id)=idealstar(nf,id,1);
zidealstarinitgen(nf,id)=idealstar(nf,id,2);
znstar